In a blender, combine the sliced strawberries, blueberries, and raspberries. Blend until smooth. If desired, strain the mixture through a fine mesh sieve to remove seeds and pulp for a smoother texture.
In a large pitcher, combine the berry puree with the freshly squeezed lemon juice and granulated sugar. Stir well until the sugar is fully dissolved.
Slowly add the sparkling water or club soda to the pitcher, stirring gently to combine.
Fill glasses with ice cubes and pour the sparkling berry lemonade over the ice.
Garnish each glass with lemon slices and fresh mint leaves before serving.